Vector Plane, Calculating Windspeed Question?

[Stanc]

Homework Statement

A plane initially flies south at a velocity of 480 km/h. Aided by a wind, the groundspeed is 528 kmh at 15 degrees east of south.

Calculate the windspeed and the direction of it

The Attempt at a Solution

I got the magnitude of 139.9 km/h but for the angle I Don't know if the angle is down below the horizontal or above the horizontal.

 

[haruspex]

I don't know which way you're measuring the angle. Pls post your working.

 

[Stanc]

Yes, Like this

 

[haruspex]

ok, that's a diagram, but somehow you calculated a speed. Presumably you created an unknown for an angle (which angle?) and wrote down some equations. pls share.

 

[Stanc]

ok, that's a diagram, but somehow you calculated a speed. Presumably you created an unknown for an angle (which angle?) and wrote down some equations. pls share.

Ok I did cos law: Wind = √ (528)^2 + (480)^2 - 2(528)(480)cos15 = 139.9

 

[haruspex]

Ok, so pick an angle in the diagram that you want to compute and write down an equation involving it and known distances.

 

[Stanc]

Ok, so pick an angle in the diagram that you want to compute and write down an equation involving it and known distances.

I used the sine law: sintheta/528 = sin15/139.9 = 77.53 degrees... So the picture where the wind goes up?

 

[haruspex]

Ok, so you are measuring the wind angle as E of N, and you get 77.5 degrees. Seems reasonable.

 

[ehild]

Well, the longest side of the vector triangle is 528 m, so the greatest angle has to be opposite to it. If one angle is 15° and the other is 77.5°, the third angle is 87.5°: the greatest angle in the triangle, and it is opposite to the side of middle length. So choose 180-77.5 as the angle of the wind.

ehild